# Area of one loop of the rose r=cos(3theta)

• Ortix
In summary, the question asks how to use double integrals to find the area of one loop of the rose r=cos(3theta). The values of -pi/6 and pi/6 for theta are chosen because they result in r=0 which is the origin, thus creating a closed loop. Since cos(3theta) is not 0 between -pi/6 and pi/6, this encloses only one loop. The conversation ends with the understanding and gratitude of the asker.
Ortix

## Homework Statement

Use double integrals to find the Area of one loop of the rose r=cos(3theta)

I know how to solve this, the only question I have is why theta is between -pi/6 and pi/6. I don't understand where those two values come from.

With theta equal to -pi/6, 3theta= -pi/2 and r= cos(3theta)= cos(-pi/2)= 0. Similarly, if theta is pi/6, 3theta= pi/2 and r= cos(3theta)= cos(pi/2)= 0. The only point with r= 0 is the origin, no matter what theta is. That means that starting at -pi/6 and going to pi/6 you have closed a loop. starting at the origin and coming back to it. Since cosine in not 0 at any point between -pi/2 and pi/2, cos(3theta) is not 0 at any point between -pi/6 and pi/6 so that encloses only one loop which is what you want.,

finally! Now i understand it! Thank you so much! :)

## What is the equation for calculating the area of one loop of the rose r=cos(3theta)?

The equation for calculating the area of one loop of the rose r=cos(3theta) is A = (3pi/8)r^2.

## What does the variable "r" represent in the equation for the area of one loop of the rose r=cos(3theta)?

In this equation, "r" represents the radius of the loop of the rose. It is equal to the cosine of three times theta.

## How do you graph the rose r=cos(3theta) to visualize the area of one loop?

To graph the rose r=cos(3theta), plot points with the coordinates (rcos(3theta), rsin(3theta)) for different values of theta. The resulting graph will have a petal-like shape and the area of one loop can be visualized within the graph.

## What is the significance of the number "3" in the equation for the area of one loop of the rose r=cos(3theta)?

The number "3" represents the number of loops in the rose. In this equation, there will be three loops in the rose, resulting in a total area of (3pi/8)r^2.

## How is the area of one loop of the rose r=cos(3theta) related to the total area of the rose?

The area of one loop of the rose r=cos(3theta) is equal to one-third of the total area of the rose. This is because the rose has three loops, and the area of one loop is (3pi/8)r^2, while the total area is (9pi/8)r^2.

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